Final answer:
To raise 20 kg of water from 40° Celsius to 80° Celsius, one would need 800 kilocalories of heat, which is equivalent to 3347.2 kilojoules.
Step-by-step explanation:
Calculating Heat Transfer for Water
To calculate the amount of heat necessary to raise 20 kg of water from 40° Celsius to 80° Celsius, we need to use the specific heat capacity of water. The specific heat capacity of water is 1 kcal/kg.°C (or 4184 J/kg.°C). To find the heat transfer in kilocalories (kcal), you multiply the mass of the water by the temperature change and the specific heat capacity:
Heat needed (kcal) = mass (kg) × temperature change (°C) × specific heat capacity (kcal/kg.°C)
Heat needed = 20 kg × (80°C - 40°C) × 1 kcal/kg.°C
Heat needed = 20 kg × 40°C × 1 kcal/kg.°C
Heat needed = 800 kcal
To convert kilocalories to kilojoules (kJ), we use the conversion factor that 1 kcal is approximately 4.184 kJ. Therefore:
Heat needed (kJ) = Heat needed (kcal) × conversion factor (kJ/kcal)
Heat needed (kJ) = 800 kcal × 4.184 kJ/kcal
Heat needed (kJ) = 3347.2 kJ
This is the amount of heat energy required to accomplish the temperature increase for 20 kg of water from 40°C to 80°C.